An Analysis of States in the Phase Space: the Anharmonic Oscillator

The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the properties of quantum systems exploiting the uncertainty principle only. Although for clarity the anharmonic oscillator is described having in mind the lattice oscillations of atoms/ions, the quantum formalism of the model and approach have general character and can be extended to any oscillating system. The results show that the harmonic energy levels split into a complex system of anharmonic energy levels dependent upon the number of terms of the Hamiltonian that describes the anharmonicity.